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2. Consider the Keynesian Beauty contest we studied in class. (Recall that in this version, as characterized in class, players seek to guess as close as possible to two-thirds of the average, and all players are the same.) (a) Show that each player picking zero is a Nash Equilibrium. (b) Show that that is the unique Nash equilibrium.

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Answer #1

The optimal strategy is to close interger to 2/3x . where x is in an integer.

X has to be less than 100 , so that player's optimal strategy has to be no more than 67.

if X is no more than 67 , players optimal strategy has be to no more than 2/3 *67...

If X is no 2/3*67, the optimal strategy of any player has to be no more than (2/3)2 *67.

iterating , unique nash eqm of this game is for every player to announce 1.

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